You can use for loops:
Operation for each item in A with each item in B:
A=[1,3,5,7,9]
B=[2,4,6,8]
C = [] #Create an empty list
for i in A: #iter each element in A
for j in B: #iter each element in B
mult = i * j
C.append(mult) #Append the result in the list C
print(C)
Operation with a random item in A with each item in B:
import numpy as np
A=[1,3,5,7,9]
B=[2,4,6,8]
C = [] #Create an empty list
for i in A: #iter each element in A
i = np.random.randint(len(A)) #Chose a random number from A
for j in B: #iter each element in B
mult = A[i] * j #Multiply a random number from A with each element in B
C.append(mult) #Append the result in the list C
print(C)